Geometric Complementarity and Irreversibility: The Exclusive Observation of Force and Energy in the State Vector K

This paper establishes a radical framework of geometric complementarity, propos-

ing that Force (F) and Energy (E) are mutually exclusive observables of a singular

spacetime state vector K. We demonstrate that the act of measuring Force through

the operator Qˆ irreversibly collapses the geometric manifold, precluding any subse-

quent measurement of the original Energy state via operator Pˆ. This fundamental

exclusion provides a purely geometric origin for the arrow of time and the non-

equilibrium nature of the universe.